Center of curvature

A concave mirror with light rays
Center of curvature

In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if the curvature is zero. The osculating circle to the curve is centered at the centre of curvature. Cauchy defined the center of curvature C as the intersection point of two infinitely close normal lines to the curve.[1] The locus of centers of curvature for each point on the curve comprise the evolute of the curve. This term is generally used in Physics regarding to study of the lenses.

It can also be defined as the spherical distance between the point at which all the rays, falling on the lens either seems to converge to it (in case of Convex Lens) or diverge from it (in case of Concave Lens) and the lens itself.

See also

Ref-notes

  1. ↑
    • Borovik, Alexandre; Katz, Mikhail G. (2011), "Who gave you the Cauchy--Weierstrass tale? The dual history of rigorous calculus", Foundations of Science, arXiv:1108.2885, doi:10.1007/s1069u9-011-9235-x

References

  • Hilbert, David; Cohn-Vossen, Stephan (1952), Geometry and the Imagination (2nd ed.), New York: Chelsea, ISBN 978-0-8284-0087-9


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